1Heat oil in 10-inch nonstick skillet over medium-high heat. Cook chicken in hot oil 5 to 8 minutes or until chicken is browned on both sides.
2Add apple juice; reduce heat to medium. Cover and cook 5 minutes. Add carrots; cover and cook 5 to 10 minutes or until juice of chicken is no longer pink when centers of thickest pieces are cut and carrots are crisp-tender.
3Remove chicken and carrots from skillet with slotted spoon; cover to keep warm. Stir mustard into liquid in skillet. Spoon mustard sauce over chicken and carrots. Sprinkle with peanuts.